Homework 1: X-ray imaging

6 thoughts on “Homework 1: X-ray imaging”

Important: I was asked after class about some weird values of $w$. The student was using NIST values for the absorption coefficient, but in that homework, soft tissue had a higher absorption coefficient than bone. This is not correct.

It is certainly correct that you need to somehow find those values, and the student’s choice of the ICRU-44 materials is good. I’ll give you a hint:

However, that table lists mass attenuation coefficients, and you need linear attenuation coefficients. Therefore, you need to multiply it with the density to obtain the linear attenuation coefficient in cm$^{-1}$. For example cortical bone at 17 keV has a linear absorption coefficient of roughly 13 cm$^{-1}$.

Muscle tissue has lower absorption coefficients than bone, and higher energies lead to lower absorption coefficients than lower energies.

The NIST tables are in log scale, and you find data only for 15 keV, 20 keV, and 30 keV. To obtain the attenuation values at 17 keV and 22 keV it is entirely sufficient to linearly interpolate between the values.

Be sure to check the values: Bone has a higher absorption coefficient than muscle tissue, and the lower-energy (17 keV) absorption coefficient is higher than the one at 22 keV.

To avoid confusion, I included a section of the NIST table with some highlights what the numbers mean. Energies are (inconveniently) given in MeV. Ignore the k-shell edges, they play no role in our consideration.

They should add up to around 0.46. At the least, you should find that $D_B$ (thickness of the bone partition) in Phantom 1 is is much smaller than 0.46cm, and that the bone partition of Phantom 3 is more than half of the total length (meaning: more than 50% bone content).

Due to rounding errors and due to differences in the spectral absorption, $D_s + D_B$ will not exactly add up to 0.46, and this is acceptable.

The x-ray machine in my lab is on the lower end of the diagnostic range with 25 to 35 kVp, and its tube current is lower than that of large TV sets. Yet it is a fully functional x-ray machine with full cabinet shielding and rigorous safety inspections by UGA’s rad safety staff.

In a CRT, therefore, the electron beam hitting the image phosphor has enough energy and enough current to produce significant and hazardous radiation levels. So what has been done — the technical solution — to keep the levels low?

There are safety circuits that provide crowbar protection when the voltages exceed the safety limits, but even within the design voltage (and the protection circuits not active), the acceleration voltage is still 27kV to 34kV, so this is not really the answer, either.